Răspunsuri

2014-07-28T10:18:29+03:00
1)0,(0x)= x/99
0,(1x)= (10+x)/99
0,(2x)=(20+x)/99
...............................
0,(8x)=(80+x)/99
0,(9x)=(90+x)/99

x/99+(10+x)/99+(20+x)/99+(30+x)/99+.....(80+x)/99+(90+x)/99=x   aducem la acelasi numitor

x+10+x+20+x+30+x+.....+80+x+90+x=99x

9x+(10+90)*9/2=99x

9x+100*9/2=99x

9x+50*9=99x

9x-99x= -450

-90x=-450

9x=45

x= 5

2)0,(6)x= 6/9*x= 2/3 *x= 2x/3

0,(3)=3/9=1/3

3,(6)=3 intregi 6/9= 3 intregi 2/3 = 11/3

2x/3 +2x -1/3= 4-2x-2 +11/3

2x/3 +2x -1/3 = 2 -2x +11/3   aducem la acelasi numitor

2x+6x-1= 6 -6x +11

8x -1= -6x +17

8x+6x=17 +1

14x=18

x=18/14= 9/7
la a) daca x=4 => 14/99+24/99+...+94/99=486/99=4.909091...
daca x=5 => 15/99+25/99+...+95/99=495/99= 5
Deci?
Stii unde cred ca ai gresit?ai luat ultimul termen 0,(8x) in loc de 0,(9x)
parerea mea e ca si la a) rezultatul tau e gresit...
gata ;)
Cel mai inteligent răspuns!
2014-07-28T10:48:24+03:00
a) 0,(1x)+0,(2x)+...+0,(9x)=x

1x/99+2x/99+...9x/99=x
(10+x)/99+(20+x)/99+...(90+x/99)=x
10/99+x/99+20/99+x/99+...+90/99+x/99=x
9*x/99+(10+20+30+...90)/99=x
9*x/99+450/99=x
9x+450=99x
90x=450
x=5

b)0,(6)x +2x-0,(3)=4-2(x+1)+3,(6)
    x*6/9+2x -3/9 =4 -2*x-2+ (36-3)/9
2x/3+2x-1/3=2-2x+33/9
2x/3+2x-1/3=2-2x+11/3
2x/3+4x=6/3+11/3+1/3
2x/3+12x/3=18/3
14x=18/3*3=18
x=18/14=9/7

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